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Closure under infinitely divisible distribution roots and the Embrechts–Goldie conjecture
We show that the distribution class ℒ(γ) \ 𝒪𝒮 is not closed under infinitely divisible distribution roots for γ > 0, that is, we provide some...
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Compound Poisson Approximations to Sums of Extrema of Bernoulli Variables
Let S n = X 1 + X 2 + · · · + X n , where X j = max( ξ j , ξ j +1 ), and ξ 1 , ξ 2 , . . . , ξ n +1 are independent Bernoulli random variables. If all P ( ξ j = 1) are...
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A Convergence Rate for Extended-Source Internal DLA in the Plane
Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an...
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On the long tail property of product convolution
Let X and Y be two independent random variables with corresponding distributions F and G on [0 ,∞ ). The distribution of the product XY , which is...
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An investigation on continuous time random walk model for bedload transport
Bedload particles in the armoring layer may experience a multi-scale effect and multiple mass transfer rates between mobile and immobile domains....
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Almost sure limit behavior of Cesàro sums with small order
Various methods of summation for divergent series have been extended to analogs for sums of i.i.d. random variables. The present paper deals with a...
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Coupling Poisson Processes by Self-Decomposability
We analyze a method to produce pairs of non-independent Poisson processes M ( t ), N ( t ) from positively correlated, self-decomposable, exponential...
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Asymptotic Behaviour of a Random Walk Killed on a Finite Set
We study asymptotic behavior, for large time n , of the transition probability of a two-dimensional random walk killed when entering into a non-empty...
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Implicit Difference Scheme of the Space-Time Fractional Advection Diffusion Equation
The space-time fractional advection diffusion equations are linear partial pseudo-differential equation with spatial fractional derivatives in time...
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Continuous time random walk models associated with distributed order diffusion equations
In this paper continuous time and discrete random walk models approximating diffusion processes associated with time-fractional and spacedistributed...
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A result on precise asymptotics for largest eigenvalues of β ensembles
The paper focuses on the precise asymptotics of the largest eigenvalues of β -Hermite ensemble and β -Laguerre ensemble. In particular, we obtain a...
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A note on the rate of returns in random walks
For one-dimensional simple symmetric random walks, we prove that the irregular set associated with the rate of returns to the origin is residual.
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A stable limit law for recurrence times of the simple random walk on the two-dimensional integer lattice
We consider the random walk of a particle on the two-dimensional integer lattice starting at the origin and moving from each site (independently of...
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Smoothing effect of compound Poisson approximations to the distributions of weighted sums
We investigate the closeness of a compound Poisson approximation to the sum S = w 1 S 1 + w 2 S 2 + ⋯ + w N S N in the Kolmogorov norm. Here S ...
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Precise Rates in the Law of the Iterated Logarithm for the First Moment Convergence
In this paper, for the partial sums with their maximums of a sequence of i.i.d. random variables, we show the precise rates in the general law of the...
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On recurrence and transience of self-interacting random walks
Let µ 1 ,...,µ k be d -dimensional probabilitymeasures in ℝ d with mean 0. At each time we choose one of the measures based on the history of the...
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Maximal Inequalities for Centered Norms of Sums of Independent Random Vectors
Let \( X_1,\,X_2 ,\,.\,.\,.\,,X_n \) be independent random...